Calibration of sensitivity and axial orthogonality for magnetometers

ABSTRACT

A reduced-cost apparatus for calibrating the sensitivity and orthogonality of a triaxial magnetometer, and a method for adjusting the distance between the two coils of a Helmholtz coil and other related parameters are described herein. A method can include positioning a calibrated magnetometer within a mounting fixture between two coils of a Helmholtz coil, the two coils arranged in mutually parallel planes and separated by the radius of the Helmholtz coil, the mounting fixture mounted such that a position of the mounting fixture is adjustable along an axis orthogonal to the mutually parallel planes; adjusting the position of the mounting fixture over at least some of the positions and measuring the magnetic field at each position to generate a set of magnetic field measurements associated with the positions; and adjusting the first distance based on the first set of magnetic field measurements. Additional apparatuses, systems, and methods are disclosed.

CLAIM OF PRIORITY

This application claims the benefit of U.S. Provisional Application Ser.No. 62/034,999, filed on Aug. 8, 2014 which application is incorporatedby reference herein in its entirety.

BACKGROUND

Understanding the structure and properties of geological formations canreduce the cost of drilling wells for oil and gas exploration.Measurements made in a borehole (i.e., downhole measurements) aretypically performed to attain this understanding, to identify thecomposition and distribution of material that surrounds the measurementdevice downhole. To obtain such measurements, magnetometers aresometimes applied to provide telemetry, ranging, and bit locationfunctions.

Currently-available systems for calibrating magnetometers often includethree-dimensional Helmholtz coils. However, such systems are often quiteexpensive. Accordingly, ongoing efforts are directed at reducing costsof magnetometer calibration systems while still maintaining quality,accuracy and sensitivity. Ongoing efforts are further directed atreducing errors that can be generated by Helmholtz coil-based systems.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a front view of an apparatus including an adjustablemechanical fixture for a one-dimensional (1D) Helmholtz coil inaccordance with some embodiments.

FIG. 2 is a side view of apparatus including an adjustable mechanicalfixture for the 1D Helmholtz coil in accordance with some embodiments.

FIGS. 3A and 3B are a front view and a side view, respectively, of amounting fixture for a magnetometer in accordance with some embodiments.

FIG. 4 is a flowchart of an example method for adjusting spacings anddistances in a 1D Helmholtz coil in accordance with some embodiments.

FIG. 5 illustrates components of a magnetic field inside a 1D Helmholtzcoil in accordance with some embodiments.

FIG. 6 illustrates coordinates of axes of a magnetometer relative tocoordinates of the mounting fixture for purposes of illustratingmisalignment errors that can be accounted for in accordance with someembodiments.

FIG. 7 illustrates orientations of axes of a magnetometer with respectto a magnetic field in accordance with some embodiments.

FIGS. 8A-8C illustrate orientations of axes of a magnetometer for use incalibrating the magnetometer in accordance with some embodiments.

FIG. 9 illustrates a system for calibrating sensitivity andorthogonality of a magnetometer in accordance with some embodiments.

FIG. 10 is a flowchart of an example method for calibrating sensitivityand orthogonality of a magnetometer in accordance with some embodiments.

FIG. 11 is a block diagram of a system in accordance with someembodiments.

FIG. 12 illustrates a wireline system embodiment of the invention.

FIG. 13 illustrates a drilling rig system embodiment of the invention.

DETAILED DESCRIPTION

To address some of the challenges described above, as well as others,apparatuses, systems, and methods for accurate and cost-effectivesensitivity and axial orthogonality calibration of a triaxialmagnetometer are described herein.

Currently-available systems that perform calibration of sensitivity andaxial orthogonality for a triaxial magnetometer often include a complex,closed-loop three-dimensional (3D) Helmholtz coil. However, the cost ofsuch systems and related maintenance is typically high. Furthermore,Helmholtz coil-based systems can be affected by various errors,including for example spacing errors between the coils of the Helmholtzcoil.

Example embodiments provide a robust, low-cost, reduced-complexityapparatus that uses a one-dimensional (1D) open-loop Helmholtz coil,while maintaining calibration accuracy by providing error control anderror mitigation techniques. Apparatuses and systems as described hereinwith respect to various embodiments can operate in standard laboratoryenvironments without the use of electromagnetic shielding, by executingnarrow-bandwidth signal processing techniques such as spectrumestimation and the lock-in amplification, rather than using more complexand costly algorithms such as the Kalman filter.

Ongoing efforts have been directed to identifying and reducing errorscaused by a Helmholtz coil-based platform. One error is related to themechanical separation between the two coils of the Helmholtz coil. For ahigh precision Helmholtz coil, the mechanical separation distancebetween the two coils is based on the radius of the Helmholtz coil.Theoretically, the radius of the Helmholtz coil is based on theassumption that the winding on the Helmholtz coil is one turn. However,typical Helmholtz coils often are wound using many turns of wires withseveral layers. Accordingly, it can be difficult to ascertain the exactmechanical center of the winding and therefore it is not trivial tospecify the correct separation distance that should be maintainedbetween the two coils.

To overcome this difficulty, some embodiments provide an adjustablemechanical fixture for a 1D Helmholtz coil. FIG. 1 is a front view, andFIG. 2 is a side view, of an apparatus 100 including an adjustablemechanical fixture for a 1D Helmholtz coil in accordance with someembodiments.

With reference to FIG. 1, the apparatus 100 includes a pair of rails 102and 104 with which the two coils 106 and 108 of the 1D Helmholtz coilare slidably engaged. The first coil 106 and the second coil 108 arearranged in mutually parallel planes 109 and spaced a distance 111 apartfrom each other along an axis A. The rails 102 and 104 are substantiallyparallel and arranged in a plane substantially orthogonal to themutually parallel planes 109 of the first coil 106 and the second coil108. The two coils 106, 108 can move along the first rail and the secondrail to adjust a distance between the two coils 106, 108. The apparatus100 includes location indicators 110 that indicate the mechanicaldistance 111 between the frames 112, 114 of the two coils 106, 108.

A mounting fixture 116 is placed on a rail 118 at a distance 115, 117between the two coils 106, 108 of the 1D Helmholtz coil, and themounting fixture 116 is configured to hold a magnetometer (not shown inFIG. 1), for example a previously-calibrated magnetometer, anon-calibrated triaxial magnetometer, etc., for further calibration asdescribed later herein. A location indicator 119 indicates themechanical position of the mounting fixture 116 on the rail 118. Therail 118 is mounted on a platform 120. Locking screws 122, 124 lock thecoils 106, 108 in place. Each of the rails 102, 104 and 118 can includemarkings that indicate distance, length, etc. The rail 118 will bearranged along an axis B substantially parallel to axis A.

FIGS. 3A and 3B are a front view and a side view, respectively, of amounting fixture 116 for a magnetometer in accordance with someembodiments. With reference to FIG. 3A, the mounting fixture 116includes a location indicator 119 for the mounting fixture 116. Themounting fixture 116 further includes an aperture 304 into which thepreviously-calibrated magnetometer, or a magnetometer that is to becalibrated, is inserted. The aperture 304 is shaped such that amagnetometer inserted into the aperture 304 is rotationally adjustableto rotate about an origin of the mounting fixture 116 to position axesof the magnetometer in at least three orientations, as will be describedin more detail below with respect to FIGS. 8A-8C.

FIG. 4 is a flowchart of an example method 400 for adjusting spacingsand distances in a 1D Helmholtz coil in accordance with someembodiments. Some operations of the example method 400 can be performedthrough processor-implemented algorithms using a computing system 918(FIG. 9), processing units 1120 (FIG. 11), control circuitry, or othercomponents, for example a signal generator 912 (FIG. 9) described laterherein. The example method 400 is described with respect to elementsdepicted in FIGS. 1-3.

The example method 400 begins with operation 402, wherein apreviously-calibrated magnetometer (not shown in FIG. 1) is positionedor inserted within the mounting fixture 116 between two coils 106, 108of the Helmholtz coil. The two coils 106, 108 are initially separated bya first distance, which is based the estimated radius of the Helmholtzcoil. The position of the calibrated magnetometer is adjustable betweenthe two coils 106, 108 of the Helmholtz coil by virtue of the calibratedmagnetometer being inserted into the mounting fixture 116, which is onrail 118 over several positions along a center axis B between the twocoils 106, 108.

An initial, estimated value for the radius of the 1D Helmholtz coil canbe decided by first measuring the thickness of the coil windings (notshown in FIG. 1) on the frame 112, 114 of the coil 106, 108, and thenadding half of this measured thickness to the measured radius of thecoil frame. The location indicators 110 can be set, as an initialmatter, one radius-length away from each other.

To estimate the error between the actual and estimated values for theradius of the 1D Helmholtz coil, and the actual and initial separationdistance between the two coils of the 1D Helmholtz coil, the apparatus,system, and methods according to various embodiments facilitatecalculation of the actual radius of the Helmholtz coil and theseparation distance between the two coils 106, 108 through a datafitting according to the following Helmholtz coil mathematicalrelationship:

$\begin{matrix}{{B\left( {x,s} \right)} = {\frac{{\varpi 0}\; {INR}^{2}}{2}\left\lbrack {\left( {R^{2} + x^{2}} \right)^{\frac{- 3}{2}} + \left\lceil {R^{2} + \left( {s - x} \right)^{2}} \right\rceil^{\frac{- 3}{2}}} \right\rbrack}} & (1)\end{matrix}$

where B(x, s) is magnetic field generated by the Helmholtz coil at pointx when the separation distance between the two coils is s, R the radiusof the Helmholtz coil, I is the electrical current flowing in the coil,N the number of the turns on the Helmholtz coil, and μ₀ the permeabilityof free space.

The example method 400 continues with operation 404, wherein theposition of the mounting fixture 116 is adjusted between the two coils106, 108 over a plurality of positions. For example, the position of themounting fixture 116 can be adjusted over all or a subset of severalpossible positions along axis B between the two coils 106, 108. Bymoving the mounting fixture 116 on rail 118, the operator can move themagnetometer, from left to right and incrementally, through the holderalong rail 118. Each incremental step can have a length of about 0.5inches, though embodiments are not limited thereto.

The example method 400 continues with operation 406, wherein a signalgenerator provides an excitation signal (e.g., a driving signal) to theHelmholtz coil to generate a magnetic field. The excitation signal willbe provided at subsequent to adjusting the mounting fixture 116 at eachof the incremental steps. The excitation signal may be provided by, forexample, the signal generator 912 (FIG. 9). The example method 400continues with operation 408, wherein the calibrated magnetometermeasures the magnetic field at each incremental step to generate a set(e.g., a first set) of magnetic field measurements associated with eachof the incremental steps and corresponding positions, for the datafitting into Equation (1). These measurements can be provided to acomputing system 918 (FIG. 9) or other circuitry to calculate the actualR and s according to Equation (1). The computing system 918 can generatea best fit curve or perform other processing based on the measurements,and the computing system 918 can determine the calculated value for Rand s or any other parameter or value based on the best fit curve.

If the calculated s is different from the distance set by the locationindicators 110, the operator will adjust distance between the two coils106, 108 in operation 408, by sliding one coil along rails 102, 104 tomake the actual separation of the two coils 106, 108 equal to the true,calculated radius of the Helmholtz coil. In some embodiments, operatorscan repeat one or more operations of the example method 400, through twoor more iterations of the example method 400, so that the actualseparation distance between the two coils will be equal to the actualradius of the Helmholtz coil.

A second error associated with Helmholtz coil-based systems in the errorassociated with the actual center location of the Helmholtz coil. Thiscenter location is the position at which a to-be-calibrated magnetometershould be placed, in order to perform calibration of that magnetometerusing the Helmholtz coil.

With the two coils having been separated with the true radius of theHelmholtz coil by the above example method 400, based on Equation (1),operators can calibrate the position for the mounting fixture 116between the two coils 106, 108. To calibrate the position, operatorswill adjust the position of the mounting fixture 116 through a pluralityof positions similar to the procedure described above with respect toexample method 400 to move the previously-calibrated magnetometer alongthe rail 118 between the two coils 106, 108. The signal generator canprovide excitation signals to generate magnetic fields, similar to theprocedure described above. The previously-calibrated magnetometer canmeasure the magnetic field at each of a plurality of positions togenerate a second set of magnetic field measurements associated with theplurality of positions. The measured magnetic field data is used by acomputing system 918 (FIG. 9), for example, or by other control ormeasurement circuitry to calculate the center location of the Helmholtzcoil with respect to the origin of the coordinates of the Helmholtzcoil, by means of data fitting into Equation (2) to find the offset x₀.

$\begin{matrix}{{B\left( {x,s} \right)} = {\frac{\mu_{0}{INR}^{2}}{2}\left\lbrack {\left\lbrack {R^{2} + \left( {x_{0} + {k\; \Delta \; x}} \right)^{2}} \right\rbrack^{\frac{- 3}{2}} + \left\lbrack {R^{2} + \left\lbrack {R - \left( {x_{0} + {k\; \Delta \; x}} \right)} \right\rbrack^{2}} \right\rbrack^{\frac{- 3}{2}}} \right\rbrack}} & (2)\end{matrix}$

where, x₀ the offset of a first coil 106 from the center point betweenthe two coils 106, 108 of the Helmholtz-coil, where the location of thefirst coil 106 is used as the origin of the Helmholtz-coil coordinates;Δx the step length (e.g., 0.5 inch), k is an integer (e.g., k=0, 1, 2 .. . , 15) that reflects the index of the current step at which themagnetic field is being measured. “First coil” in this context refers tothe nearest coil to the magnetometer at k=0. As described with respectto Equation (1), B(x, s) is the magnetic field generated by theHelmholtz coil at point x when the separation distance between the twocoils is s, R the radius of the Helmholtz coil, I is the electriccurrent flowing in the coil, N the number of the turns on the Helmholtzcoil, and μ₀ the permeability of free space.

Operators can then adjust the position of the mounting fixture 116according to a center location of the Helmholtz coil, the centerlocation having been calculated based on Equation (2). The offset x₀will be a negative number because the first coil 106 is used as theorigin of the Helmholtz coil. If the absolute value |x₀| of thecalculated x₀ is equal to R/2, then the magnetometer should be placedbetween the two coils 106, 108 at the point that is |x₀| away from thelocation of the first coil 106. The location of the first coil isindicated by the location indicator 110 on the frame 112 of the firstcoil. If |x₀| is larger than R/2, the magnetometer should be placedbetween the two coils at the point that is |x₀|+(x₀+R/2) away from thelocation indicated by the location indicator 110 on the frame of thefirst coil 106.

A third error associated with Helmholtz coil-based systems is that ofthe limited space at the center of the Helmholtz coil where the magneticfield generated by the Helmholtz coil is uniform. This error can have aparticularly deleterious effect on the accuracy of the orthogonalitycalibration.

FIG. 5 illustrates components of a magnetic field inside a Helmholtzcoil in accordance with some embodiments. With reference to FIG. 5, thevertical component BX of the magnetic field can become significant atthe edges of the measurement space delimited by the four arrows 502 ofFIG. 5, if the ratio of D to d is not sufficiently large, where D is thediameter of the Helmholtz coil, and d is the maximum dimension of theto-be-calibrated magnetometer. This can cause the magnetic field in theregion of calibration to be less uniform, leading to errors inmeasurement. However, embodiments control the amplitude of the verticalcomponents within 0.016% of the amplitude of the horizontal byconfiguring the diameters such that D≧8 d.

A fourth error associated with Helmholtz coil-based systems is that ofmachining the Helmholtz coil frame. Embodiments reduce or eliminate thiserror through use of stricter mechanical tolerance specifications forthe machine work and by installing the locking screws 122, 124 (FIG. 1)between the frames 112, 114 of the two coils 106, 108, to reduce oreliminate variations in the shape or dimension of the Helmholtz coilwith temperature and mechanical vibration.

A fifth error associated with Helmholtz coil-based systems is that ofuniformity of the wire windings on the Helmholtz coil. Embodimentsreduce or eliminate this error by winding the coil one layer afteranother as uniformly as possible with each layer being taped by a stronginsulation tape of high temperature, so that movement of the windings ofevery layer is reduced or eliminated during temperature variation andmechanical vibration.

A sixth error associated with Helmholtz coil-based systems is themechanical error of the fixture that holds the magnetometer to thecenter of the Helmholtz coil, which can also cause the error ofmisalignment. Embodiments reduce or eliminate this error by using 3-Dprinting of the supporting platform 120 and the mounting fixture 116that holds the triaxial magnetometer in the precise orientation withrespect to the central axis C of the Helmholtz coil.

A seventh error associated with Helmholtz coil-based systems is causedby the electromagnetic interference of the environment. The 1D Helmholtzcoil can be combined in some embodiments to form a system that includesa lock-in amplifier for checking the center of the to-be-calibratedmagnetometer as will be described later herein. A system according tosome embodiments can also include a spectrum analyzer for Fast FourierTransform (FFT) analysis of signals received from a to-be-calibratedmagnetometer, to reduce or eliminate electromagnetic interference as canbe generated in some testing environments. A system in accordance withsome embodiments will also include a function/arbitrary waveformgenerator for driving the Helmholtz coil to generate a sinusoidalmagnetic field, which can then be measured according to methodsdescribed later herein to determine sensitivity, misalignment errors,and other parameters or error sources associated with a magnetometer.

FIG. 6 illustrates coordinates of axes of a magnetometer relative tocoordinates of the mounting fixture 116 for purposes of illustratingmisalignment errors that can be accounted for in accordance with someembodiments. As will be appreciated, a misalignment condition 0 mayexist with respect to one or more axes wherein at least one of themagnetometer axes is shifted from, and therefore does not align with,coordinates of the mounting fixture 116.

Referring to FIG. 6, (M_(x), M_(y), M_(z)) are the coordinates of thethree magnetic axes of a triaxial magnetometer, and (x, y, z) are thecoordinates of the mounting fixture 116. Further, the origins of thesetwo coordinates are assumed to coincide at 0, which is the center of theHelmholtz coil.

Given that B is the applied magnetic field, and the components in the(x,y,z) coordinate system are Bx, By, and Bz:

$\begin{matrix}{B = {\begin{pmatrix}B_{x} \\B_{y} \\B_{z}\end{pmatrix} = {\begin{pmatrix}1 \\1 \\1\end{pmatrix}{gauss}}}} & (3)\end{matrix}$

A projection of B to the coordinates (Mx, My, Mz) can be represented byprojection matrix B2M:

$\begin{matrix}{{B\; 2\; M} = \begin{pmatrix}{BXm}_{x} & {BYm}_{x} & {BZm}_{x} \\{BXm}_{y} & {BYm}_{y} & {BZm}_{y} \\{BXm}_{z} & {BYm}_{z} & {BZm}_{z}\end{pmatrix}} & (4)\end{matrix}$

where, BXm_(x), BXm_(y) and BXm_(z) are the voltage outputs of X-axis,Y-axis and Z-axis of the magnetometer, respectively, when the appliedmagnetic field is:

$\begin{matrix}{B = {\begin{pmatrix}{Bx} \\{By} \\{Bz}\end{pmatrix} = \begin{pmatrix}1 \\0 \\0\end{pmatrix}}} & (5)\end{matrix}$

BYm_(x), BYm_(y) and BYm_(z) are the voltage outputs of X-axis, Y-axisand Z-axis of the magnetometer, respectively, when the applied magneticfield is:

$\begin{matrix}{B = {\begin{pmatrix}{Bx} \\{By} \\{Bz}\end{pmatrix} = \begin{pmatrix}0 \\1 \\0\end{pmatrix}}} & (6)\end{matrix}$

BZm_(x), BZm_(y) and BZm_(z) are the voltage outputs of X-axis, Y-axisand Z-axis of the magnetometer, respectively, when the applied magneticfield is:

$\begin{matrix}{B = {\begin{pmatrix}{Bx} \\{By} \\{Bz}\end{pmatrix} = \begin{pmatrix}0 \\0 \\1\end{pmatrix}}} & (7)\end{matrix}$

The Sensitivity and the misalignment error can be calculated by usingthe elements of the projection matrix B2M as shown by Table 1:

TABLE 1 Sensitivity and misalignment of an example magnetometer relativeto an example mounting fixture. Misalignment Misalignment MisalignmentSensitivity towards X-axis towards Y-axis towards Z-axis (V/gauss)(degrees) (degrees) (degrees) X-axis $\frac{{BXm}_{x}}{B_{x}}$$\frac{{BXm}_{y}}{{BXm}_{x}}$ $\frac{{BXm}_{z}}{{BXm}_{x}}$ Y-axis$\frac{{BYm}_{y}}{B_{y}}$ $\frac{{BYm}_{x}}{{BYm}_{y}}$$\frac{{BYm}_{z}}{{BYm}_{y}}$ Z-axis $\frac{{BZm}_{z}}{B_{z}}$$\frac{{BYm}_{x}}{{BYm}_{z}}$ $\frac{{BZm}_{y}}{{BXm}_{z}}$

Since projection matrix B2M in Equation (4) includes error informationfor both sensitivity and misalignment errors, embodiments use B2M toremove these errors through a compensation matrix C:

$\begin{matrix}{C = {{{B_{x} \cdot B}\; 2\; M^{- 1}} = {B_{x} \cdot \begin{pmatrix}{BXm}_{x} & {BYm}_{x} & {BZm}_{x} \\{BXm}_{y} & {BYm}_{y} & {BZm}_{y} \\{BXm}_{z} & {BYm}_{z} & {BZm}_{z}\end{pmatrix}}}} & (8)\end{matrix}$

If

$\quad\begin{pmatrix}{Vx} \\{Vy} \\{Vz}\end{pmatrix}$

are the voltage outputs of an example magnetometer, then the actualmagnetic field

$\quad\begin{pmatrix}{Bx} \\{By} \\{Bz}\end{pmatrix}$

will be:

$\begin{matrix}{\begin{pmatrix}{Bx} \\{By} \\{Bz}\end{pmatrix} = {B_{x} \cdot \begin{pmatrix}{BXm}_{x} & {BYm}_{x} & {BZm}_{x} \\{BXm}_{y} & {BYm}_{y} & {BZm}_{y} \\{BXm}_{z} & {BYm}_{z} & {BZm}_{z}\end{pmatrix}^{- 1} \cdot \begin{pmatrix}{Vx} \\{Vy} \\{Vz}\end{pmatrix}}} & (9)\end{matrix}$

Therefore, if a known magnetic field is applied, and the voltage outputs

$\quad\begin{pmatrix}{Vx} \\{Vy} \\{Vz}\end{pmatrix}$

can be measured, the compensation matrix C can be generated for thatmagnetometer.

Orientations of the axes of a magnetometer are defined before a magneticfield is applied to the axes for the measurement of sensitivity andmisalignment. FIG. 7 illustrates orientations of axes x, y, and z of amagnetometer with respect to a magnetic field B in accordance with someembodiments. Measurement circuitry or a measurement device, such as alock-in amplifier and a spectrum analyzer described in more detailbelow, can couple to one or more of the output of the X-axis, the outputof the Y-axis, and the output of the Z-axis to measure the magneticfield seen at each respective axis.

FIGS. 8A-8C illustrate orientations of axes of a magnetometer for use incalibrating the magnetometer in accordance with some embodiments.

Referring to FIG. 8A, the Y-axis of the magnetometer is pointingdownward when the magnetic field is applied in the positive direction ofthe X-axis of a magnetometer as shown by the arrow 802; and the positivedirection of the Z-axis of the magnetometer is pointing to the left withreference to the viewpoint of one facing the positive direction of theX-axis of the magnetometer.

Referring to FIG. 8B, the X-axis of the magnetometer is pointing to theleft, when the magnetic field is applied in the positive direction ofthe Y-axis of the magnetometer as shown by the arrow 804; and thepositive direction of the Z-axis of the magnetometer is pointing upward.

Referring to FIG. 8C, the X-axis of magnetometer is pointing to theleft, when the magnetic field is applied in the positive direction ofthe Z-axis of the magnetometer as shown by the arrow 806; and thepositive direction of the Y-axis of the magnetometer is pointingdownward.

Table 2 is example measured raw data for a magnetometer:

TABLE 2 measured raw data of an example magnetometer. Applied X-axisY-axis Z-axis magnetic output output output Orientation field (gauss)(mV RMS) (mV RMS) (mV RMS) FIG. 8A .099987 709.752 −3.3448 12.521 FIG.8B .099987 −3.983 709.994 0.503 FIG. 8C .099987 1.63 −1.906 709.036

Table 3 is calculated sensitivity and misalignment of an examplemagnetometer based on information of Table 1:

Measured Misalignment Misalignment Misalignment sensitivity towardsX-axis towards Y-axis towards Z-axis (volt/gauss) (degrees) (degrees)(degrees) X-axis 10.038705 −0.270012 1.010671 Y-axis 10.042128 −0.3214210.040592 Z-axis 10.028578 0.131717 −0.15402

Assuming that every axis of the magnetometer being calibrated receivesan applied magnetic field of 0.099987 gauss, the voltage output of themagnetometer, according to Table 2, will be:

$\begin{pmatrix}{Vx} \\{Vy} \\{Vz}\end{pmatrix} = {\frac{\sqrt{2}}{1000 \times 0.099987}\begin{pmatrix}709.752 & {- 3.983} & 1.63 \\{- 3.3448} & 709.994 & {- 1.906} \\12.521 & 0.503 & 709.036\end{pmatrix}\begin{pmatrix}0.099987 \\0.099987 \\0.099987\end{pmatrix}}$

which can be calculated to equal:

$\begin{pmatrix}1.004459 \\1.006613 \\1.016469\end{pmatrix}\mspace{14mu} {volt}$

To remove sensitivity and misalignment errors, these voltage outputs ofthe magnetometer are multiplied by a compensation matrix generated asdescribed above regarding Equations (8)-(9).

FIG. 9 illustrates a system 900 for calibrating sensitivity andorthogonality of a magnetometer in accordance with some embodiments andFIG. 10 is a flowchart of an example method 1000 that uses system 900for calibrating sensitivity and orthogonality of a magnetometer inaccordance with some embodiments.

Referring to FIG. 9, the example 1D Helmholtz coil 901 has a radius anda number of turns of windings. The 1D Helmholtz coil 901 has a firstcoil 902 and a second coil 904. The triaxial magnetometer 906 to becalibrated to remove sensitivity and misalignment errors will be placedbetween the two coils 902 and 904 according to a placement as describedearlier herein with reference to FIGS. 1-3 and Equations (1)-(2). Thetriaxial magnetometer 906 is placed at the center of the Helmholtz coilwith axes X, Y and Z being aligned to a central axis C (FIG. 1) of theHelmholtz coil, respectively one at a time as will be described in moredetail later herein and as was described above with reference to FIGS.8A-8C. In some examples, the radius of the 1D Helmholtz coil 901 can beabout 5.95 inches, and there may be 200 turns of windings, however,these are example dimensions and example embodiments are not limitedthereto.

The system 900 includes a spectrum analyzer 908, a lock-in amplifier910, and a signal generator 912. In some embodiments, the signalgenerator 912 can include an Agilent 33220A function generator,available from Agilent Technologies of Santa Clara, Calif. The spectrumanalyzer 908 can include a HP35670A spectrum analyzer available fromHewlett-Packard Co. of Palo Alto, California. The lock-in amplifier 910can include an SR850 Lock-In Amplifier available from Stanford ResearchSystems of Sunnyvale, Calif.

The signal generator 912, spectrum analyzer 908, and lock-in amplifiercan connect to computing system(s) 918, so that the computing system 918can receive measurements for use in performing any calculationsaccording to Equations (1)-(9) and Tables 1-3. In various embodiments,the computing system 918 can include a non-transitory machine-readablestorage device comprising instructions stored thereon, which, whenperformed by the computing system 918, cause the computing system 918 toperform operations, the operations comprising one or more featuressimilar to or identical to features of methods and techniques describedherein.

A machine-readable storage device, herein, is a physical device thatstores data represented by physical structure within the device.Examples of machine-readable storage devices can include, but are notlimited to, memory in the form of read only memory (ROM), random accessmemory (RAM), a magnetic disk storage device, an optical storage device,a flash memory, and other electronic, magnetic, or optical memorydevices, including combinations thereof. Executing these physicalstructures can cause the computing system 918 to perform operations ofmethods described herein.

Example method 1000 begins with operation 1002 by configuring thespectrum analyzer 908, the lock-in amplifier 910, and the signalgenerator 912. The output resistance of the signal generator 912 can beset to a high impedance, and the output of the signal generator 912 willdrive the Helmholtz coil 901 with a sinusoidal signal at a frequency of,for example, 5 Hz, and an amplitude 1.378 V_(pp). At these examplesignal generator 912 parameters, the Helmholtz coil 901 will generate asinusoidal magnetic field of amplitude 0.099987 gauss; howeverembodiments are not limited to any particular input signal parameters.

The spectrum analyzer 908 can be configured for a number of inputchannels. Operators can select various parameters and settings for thespectrum analyzer. Some example settings include DC coupling, startfrequency 0 Hz, stop frequency 12.5 Hz, and operation modepower-spectrum.

The lock-in amplifier 910 can be configured with a variety of parametersand with different traces configured. For example, the lock-in amplifier910 can be configured to include an external CLK reference, gain 50 mVRMS, with a first trace for the magnitude of the signal vector (R). Asecond trace can be used to trace the phase difference (e) between thesignal and the reference, with sync filtering on.

The example method 1000 continues with operation 1004 by aligning theX-axis of the magnetometer towards the direction of the magnetic fieldas shown by the arrow 914 of FIG. 9. In operation 1006, the switch 916is then switched to the top position as shown so that the currentsflowing in the two coils 902 and 904 are opposite to each other. Thiswill minimize the magnetic field at the center of the Helmholtz coil901.

In operation 1008, the magnetometer 906 is placed at the center of theHelmholtz coil 901 with the positive direction of the X-axis of themagnetometer being in the same direction of the magnetic field as shownby arrow 914. Next, the output of the magnetometer 906 X-axis is coupledto the A-channel input of the lock-in amplifier 910. Subsequently, theposition of the magnetometer 906 is adjusted such that the amplitude ofmagnetometer 906 X-axis reaches minimum based on examination of theR-reading of the lock-in amplifier 910. A lock screw (not shown in FIG.9) can be adjusted on the mounting fixture (not shown in FIG. 9) to fixthe magnetometer 906 at the center of the Helmholtz coil 901.

In operation 1010, the switch 916 is switched to the bottom position sothat the currents flowing in the two coils 902, 904 are in the samedirection. In operation 1012, the output of the X-axis of themagnetometer 906 is connected to the input of the spectrum analyzer 908A-channel the Y-axis is connected to the B-channel, and the Z-axis isconnected to the C-channel to measure the absolute values of thereadings of the A, B and C channels to capture BXm_(x), BXm_(y), andBXm_(z), respectively.

In operation 1014, the output of the Y-axis of the magnetometer 906 isconnected to the A-channel of the lock-in amplifier 910 to read the θvalue. If θ is near 180 degrees, then BXm_(y) is a negative value, and aminus sign is placed before BXm_(y) for use in later calculations.Similarly, the output of the Z-axis of the magnetometer 906 is connectedto the A-channel of the lock-in amplifier 910 to read the θ value, andif θ is near 180 degrees, then BXm_(z) is a negative value and a minussign is used for BXm_(z).

In operation 1016, operations 1008 and at least some of operations 1010are repeated for the Y-axis of the magnetometer 906. Subsequently, theoutput of the X-axis of the magnetometer 906 is coupled to the input ofthe spectrum analyzer 908 A-channel, the Y-axis is coupled to theB-channel, and the Z-axis is coupled to the C-channel. The absolutevalues of the readings of the A, B and C channels are examined andrecorded as BYm_(x), BYm_(y) and BYm_(z) respectively.

The output of the X-axis of the magnetometer 906 is coupled to theA-channel of the lock-in amplifier 910 to capture the θ value. If θ isnear 180 degrees, then BYm_(x) is a negative value, and a minus sign isplaced before BYm_(x). Similarly, the output of the Z-axis of themagnetometer 906 is coupled to the A-channel of the lock-in amplifier910 to read the θ value. If θ is near 180 degrees, then BYm_(z) is anegative value, and a minus sign is placed before BYm_(z).

In operation 1018, operations 1008 and at least some of operations 1010are repeated for the Z-axis of the magnetometer 906. In operation 1020,the output of the X-axis of magnetometer 906 is coupled to the input ofthe spectrum analyzer 908 A-channel, the Y-axis is coupled to theB-channel, and the Z-axis is coupled the C-channel to read the values ofthe readings of the A, B and C channels, and recorded as BZm_(x),BZm_(y) and BZm_(z), respectively. The output of the X-axis of themagnetometer 906 is connected to the A-channel of the Lock-In amplifierto read the θ value. If θ is near 180 degrees, then BZm_(x) is anegative value and a minus sign is placed before BZm_(x). Similarly, theoutput of the Y-axis of the magnetometer 906 is connected to theA-channel of the lock-in amplifier 910 to read the θ value. If θ is near180 degrees, then BZm_(y) is a negative value, and a minus sign isplaced before BZm_(y).

Having captured the elements of the projection matrix according toEquation (4), the example method 1000 continues with operation 1022,wherein the computing system 918 uses the projection matrix to calculatethe sensitivity and the misalignment according to Table 1, to calculatethe compensation matrix Equation (8). When the magnetometer is then useddownhole, the processing unit 1120 (FIG. 11) will use the compensationmatrix to correct sensitivity and misalignment errors according toEquation (9) as described earlier herein with reference to Tables 2 and3 and the corresponding discussion thereof.

FIG. 11 depicts a block diagram of features of a logging system 1100 inaccordance with various embodiments. The logging system 1100 includes amagnetometer 1104, for example a triaxial magnetometer that has beencalibrated as described above, and for which a compensation matrix hasbeen generated according to methods described earlier herein. Theprocessing unit 1120 can couple to the magnetometer 1104 to obtainmeasurements from the magnetometer 1104. The processing unit 1120 canuse the compensation matrix to adjust measurements received from amagnetometer 1104 after the magnetometer 1104 is placed downhole.

The logging system 1100 can additionally include a controller 1125, amemory 1135, an electronic apparatus 1165, and a communications unit1140. The controller 1125 and the memory 1135 can be fabricated tooperate the magnetometer 1104 to acquire measurement data as themagnetometer 1104 is operated.

Electronic apparatus 1165 can be used in conjunction with the controller1125 to perform tasks associated with taking measurements downhole withthe magnetometer 1104. The communications unit 1140 can include downholecommunications in a drilling operation. Such downhole communications caninclude a telemetry system.

The logging system 1100 can also include a bus 1127, where the bus 1127provides electrical conductivity among the components of the loggingsystem 1100. The bus 1127 can include an address bus, a data bus, and acontrol bus, each independently configured. The bus 1127 can also usecommon conductive lines for providing one or more of address, data, orcontrol, the use of which can be regulated by the controller 1125. Thebus 1127 can include instrumentality for a communication network. Thebus 1127 can be configured such that the components of the loggingsystem 1100 are distributed. Such distribution can be arranged betweendownhole components such as the magnetometer 1104 and components thatcan be disposed on the surface of a well. Alternatively, various ofthese components can be co-located such as on one or more collars of adrill string or on a wireline structure.

In various embodiments, the logging system 1100 includes peripheraldevices that can include displays 1155, additional storage memory, orother control devices that may operate in conjunction with thecontroller 1125 or the memory 1135.

In an embodiment, the controller 1125 can be realized as one or moreprocessors. The display 1155 can be arranged to operate withinstructions stored in the memory 1135 to implement a user interface tomanage the operation of the magnetometer 1104 or components distributedwithin the logging system 1100. Such a user interface can be operated inconjunction with the communications unit 1140 and the bus 1127. Variouscomponents of the logging system 1100 can be integrated with themagnetometer 1104 or associated housing to receive measurements from acalibrated magnetometer, calibrated according to methods describedearlier herein, after the calibrated magnetometer 1104 has been placeddownhole.

In various embodiments, a non-transitory machine-readable storage devicecan comprise instructions stored thereon, which, when performed by amachine, cause the machine to perform operations, the operationscomprising one or more features similar to or identical to features ofmethods and techniques described herein. A machine-readable storagedevice, herein, is a physical device that stores data represented byphysical structure within the device. Examples of machine-readablestorage devices can include, but are not limited to, memory 1135 in theform of read only memory (ROM), random access memory (RAM), a magneticdisk storage device, an optical storage device, a flash memory, andother electronic, magnetic, or optical memory devices, includingcombinations thereof. The physical structure of such instructions may beoperated on by one or more processors such as, for example, theprocessing unit 1120. Executing these physical structures can cause themachine to perform operations as described above.

In the case of ranging applications, an oscillating magnetic field canbe induced in a target that is to be located. This can be achieved witha rotating magnet on a drill bit, for example, or using anelectromagnetic source, such as a transmitter. Alternating current canalso be impressed on the casing of a target well, or the source of atime-varying magnetic field can be placed in the target well.

FIG. 12 illustrates a wireline system 1264 embodiment of the invention,and FIG. 13 illustrates a drilling rig system 864 embodiment of theinvention. Thus, the systems 1264, 1364 may comprise portions of awireline logging tool body 1270 as part of a wireline logging operation,or of a downhole tool 1324 as part of a downhole drilling operation.Thus, FIG. 12 shows a well during wireline logging operations. In thiscase, a drilling platform 1286 is equipped with a derrick 1288 thatsupports a hoist 1290.

Drilling oil and gas wells is commonly carried out using a string ofdrill pipes connected together so as to form a drilling string that islowered through a rotary table 1210 into a wellbore or borehole 1212.Here it is assumed that the drilling string has been temporarily removedfrom the borehole 1212 to allow a wireline logging tool body 1270, suchas a probe or sonde, to be lowered by wireline or logging cable 1274into the borehole 1212. Typically, the wireline logging tool body 1270is lowered to the bottom of the region of interest and subsequentlypulled upward at a substantially constant speed.

During the upward trip, at a series of depths the instruments (e.g., themagnetometer 1104 shown in FIG. 11) included in the tool body 1270 maybe used to perform measurements on the subsurface geological formationsadjacent the borehole 1212 (and the tool body 1270). The measurementdata can be communicated to a surface logging facility 1292 for storage,processing, and analysis. The logging facility 1292 may be provided withelectronic equipment for various types of signal processing, which maybe implemented by any one or more of the components of the magnetometer1104. Similar formation evaluation data may be gathered and analyzedduring drilling operations (e.g., during LWD operations, and byextension, sampling while drilling).

In some embodiments, the tool body 1270 comprises a magnetic tool forobtaining and analyzing magnetic field measurements in a subterraneanformation through a borehole 1212. The tool is suspended in the wellboreby a wireline cable 1274 that connects the tool to a surface controlunit (e.g., comprising a workstation 1254). The tool may be deployed inthe borehole 1212 on coiled tubing, jointed drill pipe, hard wired drillpipe, or any other suitable deployment technique.

Turning now to FIG. 13, it can be seen how a system 1364 may also form aportion of a drilling rig 1302 located at the surface 1304 of a well1306. The drilling rig 1302 may provide support for a drill string 1308.The drill string 1308 may operate to penetrate the rotary table 1210 fordrilling the borehole 1212 through the subsurface formations 1314. Thedrill string 1308 may include a Kelly 1316, drill pipe 1318, and abottom hole assembly 1320, perhaps located at the lower portion of thedrill pipe 1318.

The bottom hole assembly 1320 may include drill collars 1322, a downholetool 1324, and a drill bit 1326. The drill bit 1326 may operate tocreate the borehole 1212 by penetrating the surface 1304 and thesubsurface formations 1314. The downhole tool 1324 may comprise any of anumber of different types of tools including MWD tools, LWD tools, andothers.

During drilling operations, the drill string 1308 (perhaps including theKelly 1316, the drill pipe 1318, and the bottom hole assembly 1320) maybe rotated by the rotary table 1210. Although not shown, in addition to,or alternatively, the bottom hole assembly 1320 may also be rotated by amotor (e.g., a mud motor) that is located downhole. The drill collars1322 may be used to add weight to the drill bit 1326. The drill collars1322 may also operate to stiffen the bottom hole assembly 1320, allowingthe bottom hole assembly 1320 to transfer the added weight to the drillbit 1326, and in turn, to assist the drill bit 1326 in penetrating thesurface 1304 and subsurface formations 1314.

During drilling operations, a mud pump 1332 may pump drilling fluid(sometimes known by those of ordinary skill in the art as “drillingmud”) from a mud pit 1334 through a hose 1336 into the drill pipe 1318and down to the drill bit 1326. The drilling fluid can flow out from thedrill bit 1326 and be returned to the surface 1304 through an annulararea 1340 between the drill pipe 1318 and the sides of the borehole1212. The drilling fluid may then be returned to the mud pit 1334, wheresuch fluid is filtered. In some embodiments, the drilling fluid can beused to cool the drill bit 1326, as well as to provide lubrication forthe drill bit 1326 during drilling operations. Additionally, thedrilling fluid may be used to remove subsurface formation cuttingscreated by operating the drill bit 1326.

Thus, it may be seen that in some embodiments, the systems 1264, 1364may include a drill collar 1322, a downhole tool 1324, and/or a wirelinelogging tool body 1270 to house one or more magnetometers 1104, similarto or identical to the magnetometer 1104 described above with referenceto the logging system 1100. Components of the system 1100 in FIG. 11 mayalso be housed by the tool 1324 or the tool body 1270.

Thus, for the purposes of this document, the term “housing” may includeany one or more of a drill collar 1322, a downhole tool 1324, or awireline logging tool body 1270 (all having an outer wall, to enclose orattach to magnetometers, sensors, fluid sampling devices, pressuremeasurement devices, transmitters, receivers, acquisition and processinglogic, and data acquisition systems). The tool 1324 may comprise adownhole tool, such as an LWD tool or MWD tool. The wireline tool body1270 may comprise a wireline logging tool, including a probe or sonde,for example, coupled to a logging cable 1274. Many embodiments may thusbe realized.

Thus, a system 1264, 1364 may comprise a downhole tool body, such as awireline logging tool body 1270 or a downhole tool 1324 (e.g., an LWD orMWD tool body), and one or more magnetometers 1104 attached to the toolbody, the magnetometer 1104 to be constructed and operated as describedpreviously.

Any of the above components, for example the magnetometers 1104,processing units 1120, etc., may all be characterized as “modules”herein. Such modules may include hardware circuitry, and/or a processorand/or memory circuits, software program modules and objects, and/orfirmware, and combinations thereof, as desired by the architect of themagnetometer 1104 and systems 1100, 1264, 1364 and as appropriate forparticular implementations of various embodiments. For example, in someembodiments, such modules may be included in an apparatus and/or systemoperation simulation package, such as a software electrical signalsimulation package, a power usage and distribution simulation package, apower/heat dissipation simulation package, and/or a combination ofsoftware and hardware used to simulate the operation of variouspotential embodiments.

It should also be understood that the apparatus and systems of variousembodiments can be used in applications other than for loggingoperations, and thus, various embodiments are not to be so limited. Theillustrations of magnetometer 1104 and systems 1100, 1264, 1364 areintended to provide a general understanding of the structure of variousembodiments, and they are not intended to serve as a completedescription of all the elements and features of apparatus and systemsthat might make use of the structures described herein.

Applications that may include the novel apparatus and systems of variousembodiments include electronic circuitry used in high-speed computers,communication and signal processing circuitry, modems, processormodules, embedded processors, data switches, and application-specificmodules. Some embodiments include a number of methods.

It should be noted that the methods described herein do not have to beexecuted in the order described, or in any particular order. Moreover,various activities described with respect to the methods identifiedherein can be executed in iterative, serial, or parallel fashion.Information, including parameters, commands, operands, and other data,can be sent and received in the form of one or more carrier waves.

Upon reading and comprehending the content of this disclosure, one ofordinary skill in the art will understand the manner in which a softwareprogram can be launched from a non-transitory computer-readable mediumin a computer-based system to execute the functions defined in thesoftware program. One of ordinary skill in the art will furtherunderstand the various programming languages that may be employed tocreate one or more software programs designed to implement and performthe methods disclosed herein. For example, the programs may bestructured in an object-orientated format using an object-orientedlanguage such as Java or C#. In another example, the programs can bestructured in a procedure-orientated format using a procedural language,such as assembly or C. The software components may communicate using anyof a number of mechanisms well known to those skilled in the art, suchas application program interfaces or interprocess communicationtechniques, including remote procedure calls. The teachings of variousembodiments are not limited to any particular programming language orenvironment. Thus, other embodiments may be realized.

In summary, using the apparatus, systems, and methods disclosed hereinmay provide increased magnetic field measurement sensitivity over awider range of temperatures relative to conventional mechanisms. As aresult, the depth, range, and/or data rate of electromagnetic telemetrysystems may be extended, as may the range at which magnetic bodies andoscillating electromagnetic sources can be sensed remotely. Acombination of these advantages can significantly enhance the value ofthe services provided by an operation/exploration company, while at thesame time controlling time-related costs.

Further examples of apparatuses, methods, a means of performing acts,systems or devices include, but are not limited to:

Example 1 is a method comprising operations wherein any apparatuses ordevices described herein can include means for performing the method ofExample 1, and wherein the method of Example 1 comprises positioning acalibrated magnetometer within a mounting fixture between two coils of aHelmholtz coil, the two coils arranged in mutually parallel planes andbeing separated by a distance equal to an estimated radius of theHelmholtz coil, the mounting fixture being mounted such that a positionof the mounting fixture is adjustable to a plurality of positions alonga center axis of the Helmholtz coil that is orthogonal to the mutuallyparallel planes; adjusting the position of the mounting fixture betweenthe two coils over at least a subset of the plurality of positions;providing an excitation signal to the Helmholtz coil, subsequent toadjusting the position of the mounting fixture to each of the pluralityof positions, to generate a magnetic field at the calibratedmagnetometer; measuring the magnetic field using the calibratedmagnetometer to generate a first set of magnetic field measurementsassociated with the plurality of positions; and adjusting the distancebetween the two coils based on the first set of magnetic fieldmeasurements.

Example 2 includes the subject matter of Example 1, and furtheroptionally including wherein adjusting the distance comprises generatinga value for a separation distance between the two coils according to amathematical relationship between the first set of magnetic fieldmeasurements, a radius of the Helmholtz coil, and the separationdistance between the two coils; and adjusting the distance between thetwo coils to correspond to a true radius of the Helmholtz coil obtainedthrough a data fitting algorithm.

Example 3 includes the subject matter of any of Examples 1-2, andfurther optionally comprising adjusting the position of the mountingfixture subsequent to having adjusting the distance between the twocoils based on the first set of magnetic field measurements.

Example 4 includes the subject matter of Example 3, and furtheroptionally wherein adjusting the position of the mounting fixturecomprises moving the position of the mounting fixture through aplurality of positions; measuring the magnetic field, using thecalibrated magnetometer mounted inside the mounting fixture, at each ofa plurality of positions to generate a second set of magnetic fieldmeasurements associated with the plurality of positions; and adjustingthe position of the mounting fixture according to a center location ofthe Helmholtz coil, the center location having been calculated using amathematical relationship based on the second set of magnetic fieldmeasurements.

Example 5 includes the subject matter of any of Examples 1-4 andoptionally including positioning a triaxial magnetometer to becalibrated inside the mounting fixture, subsequent to calibrating theposition of the mounting fixture, the mounting fixture having anaperture configured to align the X-axis, the Y-axis, and the Z-axis of atriaxial magnetometer to the axis of the Helmholtz coil, respectivelyone axis at a time, when the triaxial magnetometer is inserted in themounting fixture; using the Helmholtz coil to apply magnetic field toeach axis of the triaxial magnetometer, one axis at a time, to generatea third set of magnetic field measurements; and generating acompensation matrix that contains data representative of misalignmenterrors based on the third set of magnetic field measurements.

Example 6 includes the subject matter of Example 5, and optionallyfurther includes wherein applying the magnetic field to the triaxialmagnetometer includes applying the magnetic field to the X-axis of thetriaxial magnetometer and recording the magnetic field measured by theX, Y and Z axes of the triaxial magnetometer; applying the magneticfield to the Y-axis of the triaxial magnetometer and subsequentlyrecording the magnetic field measured by the X, Y and Z axes of thetriaxial magnetometer; and applying the magnetic field to the Z-axis ofthe triaxial magnetometer, and subsequently recording the magnetic fieldmeasured by the X, Y and Z axes of the triaxial magnetometer.

Example 7 includes the subject matter of Example 6, and optionallyfurther includes wherein the magnetic field is applied along the X-axis,Y-axis, and the Z-axis by rotating the triaxial magnetometer betweeneach application of the magnetic field.

Example 8 includes the subject matter of Example 7, and optionallyfurther includes calculating the measured magnetic field based on thecompensation matrix.

Example 9 is a device (e.g., a Helmholtz coil or fixture or portionthereof) or other apparatus as can implement methods of Examples 1-8, orupon which Examples 1-8 can be implemented, comprising a Helmholtz coilincluding a first coil and a second coil arranged in mutually parallelplanes and spaced a distance from each other along an axis orthogonal tothe parallel planes, the first coil and the second coil slidably engagedwith a first rail and a second rail such that the first coil and thesecond coil move along the first rail and the second rail to adjust thedistance; and a mounting fixture including an aperture for mounting amagnetometer, the mounting fixture being slidably mounted to a thirdrail, the third rail passing through the first coil and through thesecond coil parallel to the axis such that the mounting fixture movesalong the third rail to adjust a distance between the mounting fixtureand each of the first coil and the second coil.

Example 10 includes subject matter of Example 9, and further optionallycomprising wherein the aperture is shaped such that a magnetometerinserted into the aperture is rotationally adjustable to rotate about anorigin of the mounting fixture.

Example 11 includes a system or portions of a system, which can includesubject matter of Examples 9-10 or means for implementing Examples 1-8,including a one-dimensional (1D) Helmholtz coil including a first coiland a second coil arranged in mutually parallel planes and spaced adistance from each other along an axis orthogonal to the parallelplanes, the first coil and the second coil slidably engaged with a firstrail and a second rail such that the first coil and the second coilslidably move along the first rail and the second rail to adjust thedistance; and a mounting fixture including an aperture for mounting amagnetometer, the mounting fixture being slidably mounted to a thirdrail, the third rail passing through the first coil and through thesecond coil parallel to the axis such that the mounting fixture slidablymoves along the third rail to adjust a distance between the mountingfixture and each of the first coil and the second coil; and amagnetometer, inserted into the aperture, to provide magnetic fieldmeasurements; and a signal generator to providing a driving signal tothe 1D Helmholtz coil.

Example 12 includes the subject matter of Example 11, and optionallyincluding one or more processors to process magnetic field measurementsof the calibrated magnetometer, and memory to store the magnetic fieldmeasurements.

Example 13 includes the subject matter of any of Examples 10-11, andoptionally further including a spectrum analyzer to analyze and displaydata representative of magnetic field measurements.

Example 14 includes the subject matter of any of Examples 10-13, andoptionally further including a triaxial magnetometer to mount inside themounting fixture; and a lock-in amplifier to couple to the triaxialmagnetometer to receive measurement signals from the triaxialmagnetometer through at least a portion of a calibration procedure.

Example 15 includes a medium or article of manufacture upon which isstored instructions that, when implemented on a machine, cause themachine to perform operations including receiving a first set ofmagnetic field measurements that have been generated by aone-dimensional Helmholtz coil having two coils with a radius, the twocoils being spaced from each other by the radius of the Helmholtz coil;and generating a calculated value for a separation distance by which thetwo coils are to be separated based on a relationship between the firstset of magnetic field measurements, the radius, and the separationdistance.

Example 16 includes the subject matter of claim 15 and optionallyincluding wherein the relationship between the first set of magneticfield measurements, the radius, and the separation distance includes amathematical relationship defined according to

${B\left( {x,s} \right)} = {\frac{\varpi \; 0{INR}^{2}}{2}\left\lbrack {\left( {R^{2} + x^{2}} \right)^{\frac{- 3}{2}} + \left\lceil {R^{2} + \left( {s - x} \right)^{2}} \right\rceil^{\frac{- 3}{2}}} \right\rbrack}$

where B(x, s) is the received magnetic field measurement at a point x, sis the separation distance, R is the radius of each of the two coils, Irepresents a value for electrical current in the Helmholtz coil, N isthe number of turns on each of the two coils, and μ₀ is the permeabilityof free space.

Example 17 includes the subject matter of any of Examples 15-16 andoptionally including instructions, that, when implemented on themachine, cause the machine to generate a best fit curve based on thefirst set of magnetic field measurements; and determine the calculatedvalue for the distance based on the best fit curve.

Example 18 includes the subject matter of any of Examples 15-17, andincluding optional further instructions to cause the machine to providethe calculated value for the distance to a display.

Example 19 includes the subject matter of any of Examples 15-18, andincluding optional further instructions to cause the machine to receivea second set of magnetic field measurements from the Helmholtz coil, theseparation distance between the two coils having been adjusted to equalthe calculated value for the separation distance; and generate acalculated value for a center of the Helmholtz coil based on arelationship between the second set of magnetic field measurements, theradius, and the separation distance.

Example 20 includes the subject matter of any of Examples 15-19 andoptionally wherein the relationship between the second set of magneticfield measurements, the radius, and the separation distance includes amathematical relationship defined according to

${B\left( {x,s} \right)} = {\frac{\mu_{0}{INR}^{2}}{2}\left\lbrack {\left\lbrack {R^{2} + \left( {x_{0} + {k\; \Delta \; x}} \right)^{2}} \right\rbrack^{\frac{- 3}{2}} + \left\lbrack {R^{2} + \left\lbrack {R - \left( {x_{0} + {k\; \Delta \; x}} \right)} \right\rbrack^{2}} \right\rbrack^{\frac{- 3}{2}}} \right\rbrack}$

where B(x, s) is the received magnetic field measurement at a point x, sis the separation distance, R is the radius of each of the two coils, Iis electrical current in the Helmholtz coil, N is the number of turns oneach of the two coils, μ₀ is the permeability of free space, x₀ is theoffset of a first coil of the two coils from the center of the Helmholtzcoil, Δx is a length, and k is an integer.

The accompanying drawings that form a part hereof, show by way ofillustration, and not of limitation, specific embodiments in which thesubject matter may be practiced. The embodiments illustrated aredescribed in sufficient detail to enable those skilled in the art topractice the teachings disclosed herein. Other embodiments may beutilized and derived therefrom, such that structural and logicalsubstitutions and changes may be made without departing from the scopeof this disclosure. This Detailed Description, therefore, is not to betaken in a limiting sense, and the scope of various embodiments isdefined only by the appended claims, along with the full range ofequivalents to which such claims are entitled.

Such embodiments of the inventive subject matter may be referred toherein, individually and/or collectively, by the term “invention” merelyfor convenience and without intending to voluntarily limit the scope ofthis application to any single invention or inventive concept if morethan one is in fact disclosed. Thus, although specific embodiments havebeen illustrated and described herein, it should be appreciated that anyarrangement calculated to achieve the same purpose may be substitutedfor the specific embodiments shown. This disclosure is intended to coverany and all adaptations or variations of various embodiments.Combinations of the above embodiments, and other embodiments notspecifically described herein, will be apparent to those of skill in theart upon reviewing the above description.

Although specific embodiments have been illustrated and describedherein, it will be appreciated by those of ordinary skill in the artthat any arrangement that is calculated to achieve the same purpose maybe substituted for the specific embodiments shown. Various embodimentsuse permutations or combinations of embodiments described herein. It isto be understood that the above description is intended to beillustrative, and not restrictive, and that the phraseology orterminology employed herein is for the purpose of description.Combinations of the above embodiments and other embodiments will beapparent to those of ordinary skill in the art upon studying the abovedescription.

What is claimed is:
 1. A method comprising: positioning a calibrated magnetometer within a mounting fixture between two coils of a Helmholtz coil, the two coils arranged in mutually parallel planes and being separated by a distance equal to an estimated radius of the Helmholtz coil, the mounting fixture being mounted such that a position of the mounting fixture is adjustable to a plurality of positions along a center axis of the Helmholtz coil that is orthogonal to the mutually parallel planes; adjusting the position of the mounting fixture between the two coils over at least a subset of the plurality of positions; providing an excitation signal to the Helmholtz coil, subsequent to adjusting the position of the mounting fixture to each of the plurality of positions, to generate a magnetic field at the calibrated magnetometer; measuring the magnetic field using the calibrated magnetometer to generate a first set of magnetic field measurements associated with the plurality of positions; and adjusting the distance between the two coils based on the first set of magnetic field measurements.
 2. The method of claim 1, wherein adjusting the distance comprises: generating a value for a separation distance between the two coils according to a mathematical relationship between the first set of magnetic field measurements, a radius of the Helmholtz coil, and the separation distance between the two coils; and adjusting the distance between the two coils to correspond to a true radius of the Helmholtz coil obtained through a data fitting algorithm.
 3. The method of claim 2, further comprising: adjusting the position of the mounting fixture subsequent to having adjusting the distance between the two coils based on the first set of magnetic field measurements.
 4. The method of claim 3, wherein adjusting the position of the mounting fixture comprises: moving the position of the mounting fixture through a plurality of positions; measuring the magnetic field, using the calibrated magnetometer mounted inside the mounting fixture, at each of a plurality of positions to generate a second set of magnetic field measurements associated with the plurality of positions; and adjusting the position of the mounting fixture according to a center location of the Helmholtz coil, the center location having been calculated using a mathematical relationship based on the second set of magnetic field measurements.
 5. The method of claim 4, further comprising: positioning a triaxial magnetometer to be calibrated inside the mounting fixture, subsequent to calibrating the position of the mounting fixture, the mounting fixture having an aperture configured to align the X-axis, the Y-axis, and the Z-axis of a triaxial magnetometer to the axis of the Helmholtz coil, respectively one axis at a time, when the triaxial magnetometer is inserted in the mounting fixture; using the Helmholtz coil to apply magnetic field to each axis of the triaxial magnetometer, one axis at a time, to generate a third set of magnetic field measurements; and generating a compensation matrix that contains data representative of misalignment errors based on the third set of magnetic field measurements.
 6. The method of claim 5, wherein applying the magnetic field to the triaxial magnetometer includes: applying the magnetic field to the X-axis of the triaxial magnetometer and recording the magnetic field measured by the X, Y and Z axes of the triaxial magnetometer; applying the magnetic field to the Y-axis of the triaxial magnetometer and subsequently recording the magnetic field measured by the X, Y and Z axes of the triaxial magnetometer; and applying the magnetic field to the Z-axis of the triaxial magnetometer, and subsequently recording the magnetic field measured by the X, Y and Z axes of the triaxial magnetometer.
 7. The method of claim 6, wherein the magnetic field is applied along the X-axis, Y-axis, and the Z-axis by rotating the triaxial magnetometer between each application of the magnetic field.
 8. The method of claim 6, further comprising: calculating the measured magnetic field based on the compensation matrix.
 9. An apparatus comprising: a Helmholtz coil including a first coil and a second coil arranged in mutually parallel planes and spaced a distance from each other along an axis orthogonal to the parallel planes, the first coil and the second coil slidably engaged with a first rail and a second rail such that the first coil and the second coil move along the first rail and the second rail to adjust the distance; and a mounting fixture including an aperture for mounting a magnetometer, the mounting fixture being slidably mounted to a third rail, the third rail passing through the first coil and through the second coil parallel to the axis such that the mounting fixture moves along the third rail to adjust a distance between the mounting fixture and each of the first coil and the second coil.
 10. The apparatus of claim 9, wherein the aperture is shaped such that a magnetometer inserted into the aperture is rotationally adjustable to rotate about an origin of the mounting fixture.
 11. A system comprising: a one-dimensional (1D) Helmholtz coil including a first coil and a second coil arranged in mutually parallel planes and spaced a distance from each other along an axis orthogonal to the parallel planes, the first coil and the second coil slidably engaged with a first rail and a second rail such that the first coil and the second coil slidably move along the first rail and the second rail to adjust the distance; and a mounting fixture including an aperture for mounting a magnetometer, the mounting fixture being slidably mounted to a third rail, the third rail passing through the first coil and through the second coil parallel to the axis such that the mounting fixture slidably moves along the third rail to adjust a distance between the mounting fixture and each of the first coil and the second coil; and a magnetometer, inserted into the aperture, to provide magnetic field measurements; and a signal generator to providing a driving signal to the 1D Helmholtz coil.
 12. The system of claim 11, further comprising: one or more processors to process magnetic field measurements of the calibrated magnetometer, and memory to store the magnetic field measurements.
 13. The system of claim 12, further comprising a spectrum analyzer to analyze and display data representative of magnetic field measurements.
 14. The system of claim 13, further comprising: a triaxial magnetometer to mount inside the mounting fixture; and a lock-in amplifier to couple to the triaxial magnetometer to receive measurement signals from the triaxial magnetometer through at least a portion of a calibration procedure.
 15. A non-transitory computer-readable medium comprising instructions that, when implemented on a machine, cause the machine to perform operations including: receiving a first set of magnetic field measurements that have been generated by a one-dimensional Helmholtz coil having two coils with a radius, the two coils being spaced from each other by the radius of the Helmholtz coil; and generating a calculated value for a separation distance by which the two coils are to be separated based on a relationship between the first set of magnetic field measurements, the radius, and the separation distance.
 16. The non-transitory computer-readable medium of claim 15, wherein the relationship between the first set of magnetic field measurements, the radius, and the separation distance includes a mathematical relationship defined according to: ${{B\left( {x,s} \right)} = {\frac{\varpi \; 0{INR}^{2}}{2}\left\lbrack {\left( {R^{2} + x^{2}} \right)^{\frac{- 3}{2}} + \left\lceil {R^{2} + \left( {s - x} \right)^{2}} \right\rceil^{\frac{- 3}{2}}} \right\rbrack}},$ where B(x, s) is the received magnetic field measurement at a point x, s is the separation distance, R is the radius of each of the two coils, I represents a value for electrical current in the Helmholtz coil, N is the number of turns on each of the two coils, and μ₀ is the permeability of free space.
 17. The non-transitory computer-readable medium of claim 16, further comprising instructions, that, when implemented on the machine, cause the machine to: generate a best fit curve based on the first set of magnetic field measurements; and determine the calculated value for the distance based on the best fit curve.
 18. The non-transitory computer-readable medium of claim 15, further comprising instructions that, when implemented on a machine, cause the machine to perform operations including: providing the calculated value for the distance to a display.
 19. The non-transitory computer-readable medium of claim 15, further comprising instructions that, when implemented on a machine, cause the machine to perform operations including: receiving a second set of magnetic field measurements from the Helmholtz coil, the separation distance between the two coils having been adjusted to equal the calculated value for the separation distance; and generating a calculated value for a center of the Helmholtz coil based on a relationship between the second set of magnetic field measurements, the radius, and the separation distance.
 20. The non-transitory computer-readable medium of claim 19, wherein the relationship between the second set of magnetic field measurements, the radius, and the separation distance includes a mathematical relationship defined according to: ${{B\left( {x,s} \right)} = {\frac{\mu_{0}{INR}^{2}}{2}\left\lbrack {\left\lbrack {R^{2} + \left( {x_{0} + {k\; \Delta \; x}} \right)^{2}} \right\rbrack^{\frac{- 3}{2}} + \left\lbrack {R^{2} + \left\lbrack {R - \left( {x_{0} + {k\; \Delta \; x}} \right)} \right\rbrack^{2}} \right\rbrack^{\frac{- 3}{2}}} \right\rbrack}},$ where B(x, s) is the received magnetic field measurement at a point x, s is the separation distance, R is the radius of each of the two coils, I is electrical current in the Helmholtz coil, N is the number of turns on each of the two coils, μ₀ is the permeability of free space, x₀ is the offset of a first coil of the two coils from the center of the Helmholtz coil, Δx is a length, and k is an integer. 